T.C. 28 April 2009 Big Idea Negative numbers help us to model many real world situations. Essential Question #4 How do I multiply and divide integers?
Mathematical Reflection: p.66
Write a strategy for multiplying two integers. Be sure to consider all possible combinations of positive integers, negative integers, and 0.Verify your strategy by finding the following products:
a. -13 x 7:-13 x 7 = -91
A strategy for solving this is that you always know that a negative times a positive equals a negative. So then you can a simple multiplication problem like 13 x 7 and then add the (-), because it will always be negative.
b. 11 x –20:11 x –20 = -220
A strategy for solving this problem would be that you always know that a positive times a negative equals a negative. So then you can a simple multiplication problem like 11 x 20 and then add the (-), because it will always be negative.
c. –12 x 0:-12 x 0 = 0
A strategy is that if you times something by zero its always going to be zero. Because 12 times 0 is just twelve zeros, so 0,0,0,0,0,0,0,0,0,0,0,0 and all those added together equal… 0!
d. –18 x –22:-18 x –22 = 396
A strategy for this is it will always be positive because the 2 negatives cancel each other out so you are left with a simple multiplication problem, which you can then solve.
Write a strategy for dividing two integers. Be sure to consider all possible combinations of positive integers, negative integers, and 0.Verify your strategy by finding the following quotients:
a. 126 / -9:126 / -9 = -14
A strategy is that becausea positive divided by a negative is always a negative, so you then just do a simple division problem.
b. –36 / -12:-36 / -12 = 3
A strategy for this is that a negative divided by a negative is always a positive because the two negatives cancel each other out so then you can just do a simple division problem.
c. –2592 / 32:-2592 / 32 = -81
A strategy for this is that a negative divided by a positive is always going to be a negative so then you can forget about the (-) or (+) signs and do a simple division problem and then just add a (-) sign.
d. 0 / 8:0 / 8 = 0
A strategy for this would be that if you ever have zero divided by somethingit will always be 0. Because0 divided by 8 is 0 because you can’t divide 0 it will always be zero.
Summary: There are different strategies for different multiplication problems and division problems but once you know what the out come has to be then you can just do a simple (x) or (/) problem and add a (-) or (+) on if needed.
(-) x (-) = (+)
(+) x (-) = (-)
(+) x (+) = (+)
(-) x (+) = (-)
and the same for (/) except not a (x) and a (/) instead.
T.C.
28 April 2009
Big Idea
Negative numbers help us to model many real world situations.
Essential Question #4
How do I multiply and divide integers?
Mathematical Reflection: p.66
Write a strategy for multiplying two integers. Be sure to consider all possible combinations of positive integers, negative integers, and 0.Verify your strategy by finding the following products:
a. -13 x 7: -13 x 7 = -91
A strategy for solving this is that you always know that a negative times a positive equals a negative. So then you can a simple multiplication problem like 13 x 7 and then add the (-), because it will always be negative.
b. 11 x –20: 11 x –20 = -220
A strategy for solving this problem would be that you always know that a positive times a negative equals a negative. So then you can a simple multiplication problem like 11 x 20 and then add the (-), because it will always be negative.
c. –12 x 0: -12 x 0 = 0
A strategy is that if you times something by zero its always going to be zero. Because 12 times 0 is just twelve zeros, so 0,0,0,0,0,0,0,0,0,0,0,0 and all those added together equal… 0!
d. –18 x –22: -18 x –22 = 396
A strategy for this is it will always be positive because the 2 negatives cancel each other out so you are left with a simple multiplication problem, which you can then solve.
Write a strategy for dividing two integers. Be sure to consider all possible combinations of positive integers, negative integers, and 0.Verify your strategy by finding the following quotients:
a. 126 / -9: 126 / -9 = -14
A strategy is that because a positive divided by a negative is always a negative, so you then just do a simple division problem.
b. –36 / -12: -36 / -12 = 3
A strategy for this is that a negative divided by a negative is always a positive because the two negatives cancel each other out so then you can just do a simple division problem.
c. –2592 / 32: -2592 / 32 = -81
A strategy for this is that a negative divided by a positive is always going to be a negative so then you can forget about the (-) or (+) signs and do a simple division problem and then just add a (-) sign.
d. 0 / 8: 0 / 8 = 0
A strategy for this would be that if you ever have zero divided by something it will always be 0. Because 0 divided by 8 is 0 because you can’t divide 0 it will always be zero.
Summary:
There are different strategies for different multiplication problems and division problems but once you know what the out come has to be then you can just do a simple (x) or (/) problem and add a (-) or (+) on if needed.
(-) x (-) = (+)
(+) x (-) = (-)
(+) x (+) = (+)
(-) x (+) = (-)